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8/8/2019 Ch23 - Retaining wall Figures
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SlidingFriction
PassivePressure
Active pressure
Figure 23.1 Forces and pressures acting between an earth retaining structure and the ad- jacent ground.
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WallBackfill
b
At-restlateralearth pressure
K 0 H
H
Figure 23.2 At-rest pressure acting on a retaining wall.
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Active Condition
At-Rest Condition
FailurePlane
'
c
' z ' x ' x
AB
FailurePlane
Figure 23.3 Changes in the stress conditions in a soil as it transitions from the at-restcondition to the active condition.
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Movement
Shear-failurePlanes
45 + /2
Figure 23.4 Development of shear failureplanes in the soil behind a wall as it transi-tions from the at-rest condition to the activeconditon.
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Movement Awayfrom B ackfill
Movement Toward Backfill0
K p
K a
K o
C o e
f f i c i e n
t o
f L a
t e r a
l E a r t
h P r e s s u r e
Figure 23.5 Effect of wall movement onlateral earth pressure in sand.
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' z ' x ' x
A
B
FailurePlane
PassiveCondition
c
'
At-RestCondition
FailurePlane
Figure 23.7 Changes in the stress condi-tion in a soil as it transitions from the at-restcondition to the passive condition.
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Active Pressure
SlidingFriction
PassivePressure
Figure 23.8 Active and passive pressures acting on a cantilever retaining wall.
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45 /2
W / b
T / b
N / b
V p / b
P p / b
(a)
(b)
H
45 + /2
W / b
T / b
N / b
V a / bP a / b
H
Figure 23.9 Free body diagram of soil behind a retaining wall using Rankine s solution:(a) active case; and (b) passive case.
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(a) (b)
Figure 23.10 Comparison between (a) the-oretical and (b) observed distributions of earth pressures acting behind retaining struc-tures.
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13
44 kN/m
136 kN/m
6 m
Figure 23.11 Results from Example 23.2.
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V a / b
H
wP a / b
Figure 23.12 Parameters for Coulomb s active earth pressure equation. Walls inclinedin the opposite direction have a negative . V a /b normally acts in the direction shown,
thus producing a positive w .
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12
c = 0 = 32
= 19.8 kN/m 3
5.60 m2
Figure 23.13 Retaining wall for Example 23.4.
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H
H c
Figure 23.14 Theoretical active pressuredistribution in soils with cohesion ( c 0,
0).
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H
Figure 23.15 Theoretical distribution of passive earth pressure in soils with cohesion(c 0, 0).
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80
60
40
20
0
160
140
120
100
80
60
40
20
0
0
5
10
25
20
15
10
5
010 20 30
5 Gv
(kN/m3)
6 : 1 3 : 1 2 : 1 1 : 112
2 :1 max.
3 :1 max.
2 :1 max.
Slope Angle
Gv
(lb/ft3) H
H
3
2
1
4
5
4
1
3 2
G h(kN/m 3)
G h(lb/ft 3)
40
Figure 23.16 Charts for estimating the loads acting against a retaining wall beneath a planarground surface (Adapted from Terzaghi and Peck, 1967).
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H 1
H 1 = 0
Soil Type 1 Soil Type 2 Soil Type 3
Gv = 0
Slope 1 12 : 1
Slope 1 12 : 1Slope 1 12 : 1
3 :16 :1
3 :1
6 :1
34 : 11
12 : 11
H 1 / H
160
140
120
100
80
60
40
20
0 0.2 0.4 0.6 0.8 1.0
0 0.2 0.4 0.6 0.8 1.0
G(lb/ft) 3
0 0.2 0.4 0.6 0.8 1.0
25
20
15
10
5
0
0 0.2 0.4 0.6 0.8 1.0
80
100
60
40
20
Soil Type 4 Soil Type 5
H 1 / H
G(lb/ft) 3
G(kN/m 3)
G(kN/m 3)
15
10
5
0
H
H
H 1
H
0 0.2 0.4 0.6 0.8 1.0
Max Slope 2 : 1
Max Slope 3 : 1Max Slope 2 : 1
12 : 111
2 : 1134 : 1134 : 11
2 :13 :1 2 :1
3 :12 :1 2 :1
3 :1
34 : 11 2 :1 3 :1
6 :1
34 : 11
2 :13 :1
6 :16 :1
34 : 11 3 :12 :1
Legend
Gh
Gv
Figure 23.17 Charts for estimating the loads acting against a retaining wall below a ground surfacethat is sloped and then becomes level. For soil type 5, use an H value 4 ft (1 m) less than the actualheight (Adapted from Terzaghi and Peck, 1967).
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Point LoadSurcharge
Uniform
Surcharge
Figure 23.18 Typical surcharge loads near a retaining wall.
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q = 13.0 kPa2.5 m
(kPa)
= 31 = 0.3
c = 09.0 m
0 5 10 15 20
Due toUniformLoad Due to
Point Load
1
2
3
4
z
( m
)
1000 kN
Figure 23.19 Proposed retaining wall with surcharge load for Example 23.6.
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Pressure due to Backfill(Lateral Earth Pressure)
Pressure due to Groundwater(Hydrostatic Pressure)
u
Figure 23.20 Theoretical lateral pressuredistribution with shallow groundwater table.
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Groundwaterat b
b
Pressure due to Backfill Hydrostatic Pressure
Groundwaterat a
5.3 m
2.5 m
a
b
a
6 m
Figure 23.21 Retaining wall for Example 23.7.